Mathematics
EN FR
← Retour à la révision

Fluidité · Pack A

7.7 Shape and Measure

Répondez à chaque question. Montrez les calculs si nécessaire.

Bronze

  1. A rectangle has perimeter 16 cm. Give two different pairs of whole-number side lengths that would produce this perimeter. Verify each pair by adding.

  2. A triangle has sides 5 cm, 7 cm and 9 cm. What is its perimeter? Show the addition.

  3. A rectangle has area 24 cm² with whole-number sides. Give three different (length, width) pairs. Verify each by multiplying.

  4. Find the area of a rectangle with length 9 cm and width 4 cm. Show the multiplication and write the units.

  5. A right-angled triangle has base 6 cm and height 8 cm. Find its area. Explain why you halve the rectangle formula.

  6. A shape has 4 sides and 2 lines of symmetry. Name two possibilities and justify each.

  7. A cuboid has length 4 cm, width 3 cm and height 2 cm. Find its volume by multiplying length × width × height. Show each step.

  8. A regular polygon has perimeter 35 cm and each side is 7 cm. Find the number of sides by dividing. State the name of the polygon.

  9. A rectangle has perimeter 26 cm and length 8 cm. Find the width by calculation. Then find the area.

  10. A compound shape is made from two rectangles. Rectangle A is 6 cm × 4 cm. Rectangle B is 3 cm × 2 cm. Find the total area by calculating each area separately then adding.

Silver

  1. Find the area of a parallelogram with base 9 cm and perpendicular height 5 cm.

  2. Find the area of a trapezium with parallel sides 5 cm and 9 cm and perpendicular height 4 cm.

  3. Find the volume of a cuboid with length 5 cm, width 4 cm and height 3 cm.

  4. Find the surface area of a cuboid with length 5 cm, width 3 cm and height 2 cm.

  5. A compound shape is made from a rectangle 8 cm by 6 cm with a 2 cm square removed from one corner. Find the area.

  6. Find the perimeter of a regular 8-sided polygon with side length 5 cm.

  7. A net is folded to make a cuboid with dimensions 4 cm × 3 cm × 2 cm. How many faces does it have and what is its surface area?

  8. A triangle has base 8 cm and area 28 cm². Find its perpendicular height.

  9. How many faces, edges and vertices does a triangular prism have?

  10. A rectangle has a perimeter of 30 cm and a length of 9 cm. Find its width and hence its area.

Gold

  1. A rectangle has area 24 cm² and width 3 cm. Find its perimeter.

  2. A square has side 1.5 cm. Find its area in cm² and then convert it to mm².

  3. A trapezium has parallel sides 4 cm and 8 cm. Its area is 30 cm². Find its perpendicular height.

  4. A compound L-shape is formed by a large rectangle 10 cm by 8 cm with a smaller rectangle 4 cm by 3 cm cut from one corner. Find the area of the L-shape.

  5. A rectangle has length $(x + 3)$ cm and width $(2x)$ cm. Write an expression for its perimeter and simplify.

  6. A rectangular garden is 3.2 m long and 2.5 m wide. Find its area in m² and convert the answer to cm².

  7. A square has area 49 cm². Find its perimeter.

  8. Find the surface area of a cuboid with dimensions 7 cm × 4 cm × 3 cm.

  9. A rectangle is 12 cm long and 5 cm wide. What is three-quarters of its area?

  10. A triangular prism has a triangular cross-section with base 6 cm and height 4 cm, and a length of 10 cm. Find its volume.

Platinum

  1. A rectangle has length $(2x + 1)$ cm and width $(x - 2)$ cm. Its perimeter is 34 cm. Find $x$ and hence find the area.

  2. A compound shape is made by joining a rectangle 10 cm × 6 cm and a triangle with base 6 cm and height 4 cm along a shared edge of length 6 cm. Find the total area.

  3. A cuboid fish tank is 1.2 m long, 0.5 m wide and 0.4 m deep. It is filled to three-quarters of its height. Find the volume of water in litres. (1 m³ = 1 000 litres.)

  4. A square tile has perimeter 28 cm. Tiles are arranged in a 4 × 5 grid with no gaps. Find the total area of the tiled surface in cm² and convert to m².

  5. Two identical trapeziums, each with parallel sides 5 cm and 11 cm and perpendicular height 6 cm, are placed together along their longer parallel side to form a parallelogram. Find the area of the parallelogram.

  6. A rectangle has length 10 cm and width 8 cm. Both dimensions are increased by 20%. Find the new area and the percentage increase in area.

  7. A cuboid has volume 120 cm³. Its length is 6 cm and its width is 4 cm. Find its height and hence its surface area.

  8. The area of a square is 196 cm². Express 196 as a product of prime factors, and hence write down the exact side length of the square.

  9. A path of uniform width 2 cm runs around the outside of a rectangle 10 cm × 6 cm. Find the area of the path alone.

  10. A cube has surface area 216 cm². Find its side length, volume and express the volume in litres.